The Collatz Bench

tree

river

this trajectory

—

stopping time σ(n) — how far each number falls —

σ(n) scatter

histogram

an open question The Collatz conjecture (Lothar Collatz, 1937) says every positive integer reaches 1 under n → n/2 if even, 3n+1 if odd. Still unproven in 2026 — yet checked by computer past 2⁶⁸, with 0 counterexamples. Erdős said: "Mathematics is not yet ready for such problems." This bench checks; it never claims a proof.

start at n

the field — tree depth (what's drawn)

verified forward range (what's checked)

checking n ≤ 10,000 · pill / records / scatter

this trajectory

start n—

steps to 1—

peak—

records — total-stopping-time setters

Live-computed up to the verified range, matched to OEIS A006877 (steps) & A006884/A025586 (peaks). n=27's row peaks — the 23→111 jump no smaller start makes.

does it halt? → The Mill

The conjecture is a halting question: run n→n/2 | 3n+1 as a program — every tested input halts at 1, but no machine can promise it always will. The workshop's honest brush with undecidability.

What this proves — and what it can't.
Proven live: the records reproduce the literature exactly · two independent constructions (forward re-walk & backward tree) agree · the 3n−1 map is caught failing — it falls into the 5→7→10→14→20 loop, never reaching 1.
NOT proven by anyone: that every n reaches 1. That is the open conjecture — checked here to your range, with 0 counterexamples, and honestly labelled.
The number-theory sibling of The Ulam Spiral & The Best Rational.